For the last few years, many countries, but mainly the US, have been complaining that China saves too much. By implication, it must also invest too much, over 40 per cent of its GDP. Too much? Whatever does that mean, ask three very annoyed Chinese economists -- whose affiliations, quite unusually for NBER, have not been mentioned.

In a recent paper*, Chong-En Bai, Chang-Tai Hsieh, and Yingyi Qian say this is a nonsensical notion, and set about explaining why they think so. A low income country and with poor skills can't invest too much, they say, which is probably right because the capital-labour ratio is still very low in such places. But they admit that a better way of judging is to see what the rate of return on capital is. If it is low, it means "too much" investment and if it is not low, it does not mean too much investment.

"A natural metric to use is the return to capital... the investment rate in China might be high precisely because the return to capital in China is high." In other words, the cause and effect may be the opposite of what everyone thinks.

The authors ask three questions. First, whether the rate of return has been declining. Second, whether it is lower than in the rest of the world. And third, whether China's investment pattern's been lopsided, both sectorally and regionally.

Their paper, they say, "measures the return to capital in China, calculated using data on the share of capital in total income, the capital-output ratio (where both capital and output are measured at market prices), the depreciation rate, and the growth rate of output prices relative to capital prices." They concede that their main problem is data, which could be quite dodgy.

They have used the most recent data from China's National Bureau of Statistics, collected during the 2004 census. And capital stock is calculated at market prices.

Somehow surmounting these data hurdles, the authors eventually conclude that although between 1979 and 1992, the aggregate rate of return was 25 per cent, it has since declined modestly to a still respectable level of 20 per cent. It has remained there since 1998. So why complain?

"These rates of return are above rates of return for most advanced economies calculated on similar basis," they say and "all in all, our findings on the returns to capital provide no evidence to believe that China invests too much at the aggregate level."

Not just that. It seems "investment in China is being distributed more efficiently than in the past", but that the efficiency of investment allocation across provinces and across major sectors is a little suspect.

As to the method, they say, "What matters for determining return to capital is not the marginal physical product of capital, but rather the ratio of the marginal revenue product of capital to the price of capital."

This is right, of course, but the problem is that no one really quite knows what the real price of capital is in China and certainly not what the marginal revenue product is. So the even if you can devise an equation, getting it to work would be a big problem.

The authors also assume, for no particular reason that "the price of capital grows at the same rate as the price of output." They also assume that the labour share is 50 per cent. They take depreciation at 10 per cent, and the nominal capital-output ratio is 1.67. Firms are price takers.

If you do all this you get a real return to capital as 20 per cent. The question is: who, apart from the authors, believes it?

* The Return to Capital in China,NBER Working Paper No. 12755, December 2006